# 2- stage DDM

Hi -

This questions has been discussed in another thread but I am not sure I understand as explained in the Schweser solutions (Exam 1 - Afternoon session solution).

Question:

Assume the Wansch Corporate is expected to pay a dividend of $2.25 per share this year. Sales and profit for Wansch are forecasted to grow at a rate of 20% for two years after that, and then grow at 5% per year forever. Dividend and sales growth are expected to be equal. If Wansch’s shareholders require a 15% return, the per-share return value of Wansch’s common stock based on the DDM is closest to.

My solution is:

CF0 = $2.25 is received at the end of the this current year (so no growth rate will be be applied to this divided but WILL be discounted back by 1 year to bring it back to PV)

At the end of current year (discussed above), we are still expected 2 years of 20% growth to the end-of-the-year dividend of $2.25. This will take us to the end of year 3.

Therefore:

CF1 = $2.25 * (1 + 0.20) = $2.7 - this cash flow is due at the end of year 2 and will be discount back by 2 years

CF2 = $2.25 * (1+ 0.20) * (1+0.20) = $3.24 and will be discounted back by 3 years

Terminal Value:

Now we are expecting perpetual growth of 5%.

Therefore: the Present Value of the Terminal Value i.e. the value at the end of year 3 is:

Terminal Value = CF2 * (1+0.05)/(0.15-0.05) = $3.24 * (1.05) / (0.10) = $110.16

This terminal value will be discounted back by 3 years. Therefore, value of the stock is:

V = [ $2.25 / (1+ 0.15) ] + [ $2.7 / (1+ 0.15)^{2}] + [$3.24/(1.15)^{3}] + [$110.16/ (0.15 - 0.05) * (1.15)^{3}]

= $1.95 + $2.04 + $4.92 + $951.6

= $960.5

What is wrong with this approach? Am I interpreting the question incorrectly?

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I haven’t read the whole thing, but perhaps start with how did you manage to calculate $110.16 for the formula above?

bazz

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I think you’ll want to revise how/why you calculated $110.16

Pretty sure the terminal value of the stock at the end of year 3 is calculated as 3.402 / (.15 - .05) = 34.02 + the dividend recieved at the end of year three –> $37.26

I calculated a value that the stock is worth $33.31 as of today.

I’m also pretty confident that when you read a problem that says “it will pay it

THISyear, that it turns into D1 and not D0. Which means you’ll need to discount the $2.25 back by 1.15 to arrive at P0EDIT: I found where you went wrong:

Not only is the value of $110.16 incorrect, but, you’re growing it too many times. According to you, the terminal value is already $110.16, but then you’re growing that again by dividing it by 0.1 and then once more by multiplying it by 1.15

^{3}. stop stop stop…The terminal value is always given as Po = D1 / (r - g) which works out to 3.402 / (.15 - .05) = 34.02. Then you should have

addedthe 34.02 to the final dividend recieved in the high growth period of 3.24 to get a total D3 present value of 37.26 and then you would discount $37.26 back three times by 15%. You have handled the first two dividends correctly though.¯\_(ツ)_/¯ It be like that sometimes.